Really, doesn't matter if you are at BW, BC or YC as far as views to Illuminations go. Can you see them from your room, depends on where your room is located, if it's one that faces into the resort or our to the parking lot, you aren't going to be able to see them from BC. From BW I'm not sure. All are easy enough to step outside your room to see them.
Yes, there is still BW type entertainment on the BW. Again, easy enough to get to from all three resorts.
You can request connecting rooms, you are not guaranteed to get them at any of the resorts.
Define a hike to get anywhere. YC/BC are really just one big resort. YC facing the BW would probably be closer to HS then BC facing Epcot. BC facing Epcot is going to be closer to Epcot. BW, depends on your room location since if you look at it, it looks like it is pretty much the same length as YC/BC combined. The rooms are pretty much scattered all over all the resorts as far as standard, water and garden views. You can request close to elevator or close to lobby but again it's just a request.
MK. you can bus to or you can walk through Epcot and take the monorail.
AK you bus.